Problem: $h(n) = 3n+6-4(g(n))$ $g(x) = 5x^{3}+3x^{2}$ $f(n) = -3n^{2}-2(h(n))$ $ f(g(0)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(0)$ . Then we'll know what to plug into the outer function. $g(0) = 5(0^{3})+3(0^{2})$ $g(0) = 0$ Now we know that $g(0) = 0$ . Let's solve for $f(g(0))$ , which is $f(0)$ $f(0) = -3(0^{2})-2(h(0))$ To solve for the value of $f$ , we need to solve for the value of $h(0)$ $h(0) = (3)(0)+6-4(g(0))$ To solve for the value of $h$ , we need to solve for the value of $g(0)$ $g(0) = 5(0^{3})+3(0^{2})$ $g(0) = 0$ That means $h(0) = (3)(0)+6+(-4)(0)$ $h(0) = 6$ That means $f(0) = -3(0^{2})+(-2)(6)$ $f(0) = -12$